Abstract
The authors recently proved that for a semiprime ring without $2$-torsion, a nilpotent derivation must have odd nilpotency. In this paper, we show the intriguing phenomenon that for a semiprime ring with characteristic 2, the nilpotency of a nilpotent derivation must be of the form ${2^n}$. Combining these two results, we show that for a general semiprime ring with no torsion condition, the nilpotency of a nilpotent derivation is either odd or a power of 2.
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